Alvarus, Thomas, Liber de triplici motu, 1509

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                  <pb chead="Secunde partis." file="0054" n="54"/>
                maius fuit pars maioris: ſed remanet h. maiꝰ / er-
                  <lb/>
                go erat pars maioris et erat pars ipſius .hd. / er-
                  <lb/>
                go .hd. eſt maius / quod fuit ꝓbandum. </s>
                <s xml:id="N15456" xml:space="preserve">Et ſic patet
                  <lb/>
                prima pars. </s>
                <s xml:id="N1545B" xml:space="preserve">iam probatur ſecūda pars et volo / 
                  <lb/>
                inter b. et d. ſit ꝓportio f. et acquirat b.a. ſupra ſe:
                  <lb/>
                et d. acquirat c. ſupra ſe: ſit ipſius a. acquiſiti b.
                  <lb/>
                maiori termino ad ipſum c. acquiſituꝫ minori ter­
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                mino proportio g. minor ꝓportione f. / tunc dico / 
                  <lb/>
                ꝓportio f. inter illos terminos diminuitur: ita 
                  <lb/>
                in fine ipſius .ab. ad ipſum .cd. erit minor ꝓportio
                  <lb/>
                quam f. </s>
                <s xml:id="N1546C" xml:space="preserve">Quod ſic ꝓbo et capio / h. latitudinem ad
                  <lb/>
                quam a. habet ꝓportionem f. / et arguo ſic / ſi quãdo
                  <lb/>
                b. acquireret h. adhuc inter illos terminos ma-
                  <lb/>
                neret ꝓportio f. puta inter .ab. et .hd. / vt patet
                  <lb/>
                ex quinto correlario quinte concluſionis ſecundi
                  <lb/>
                capitis huius: ſed modo .cd. eſt maius ipſo .hd. / er­
                  <lb/>
                go ipſius .ab. ad ipſum .cd. eſt minor ꝓportio quã
                  <lb/>
                ad ipſum .hd. / et per conſequens minor quaꝫ f. / qḋ
                  <lb/>
                fuit ꝓbandum. </s>
                <s xml:id="N1547F" xml:space="preserve">Sed reſtat probare /  ipſum .cd.
                  <lb/>
                eſt maius ipſo .hd. / quod ſic oſtenditur / quia dem-
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                pto eodem communi ab .hd. et a.cd. / videlicet dē-
                  <lb/>
                pto ipſo d. ex .cd. manet maius quam ex .hd. / igi-
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                tur .cd. eſt maius ipſo .hd. </s>
                <s xml:id="N1548A" xml:space="preserve">Patet cõſequentia ex
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                dignitate arithmetica: et probatur aſſumptuꝫ / q2
                  <lb/>
                ex .hd. manet h. et ex .cd. manet c. adequate / vt con­
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                ſtat et a. habet maiorem proportionem ad h. quã
                  <lb/>
                idem a. habeat ad c. / vt poſitum eſt: igitur c. eſt ma­
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                ius h. et c. manet ex .cd. et h. ex .hd. / igitur qḋ ma-
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                net ex .cd. eſt maius illo quod manet ex .hd. eodeꝫ
                  <lb/>
                communi dempto / quod fuit probanduꝫ. </s>
                <s xml:id="N1549B" xml:space="preserve">Et ſic pa­
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                tet correlarium.
                  <note position="left" xlink:href="note-0054-01a" xlink:label="note-0054-01" xml:id="N155E5" xml:space="preserve">4. correl.</note>
                </s>
                <s xml:id="N154A5" xml:space="preserve">¶ Sequitur quarto /  quando in­
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                ter aliquos terminos eſt proportio maioris ine-
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                qualitatis: et vtro termino creſcente: ꝓportio ī­
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                ter eos augetur: tunc inter acquiſitum maiori ter­
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                mino et acquiſitum minori eſt ꝓportio quaꝫ ſit ꝓ­
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                portio inter illos terminos quibus ſit acquiſitio
                  <lb/>
                </s>
                <s xml:id="N154B3" xml:space="preserve">Si auteꝫ ꝓportio inter datos terminos diminua­
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                tur creſcente vtro: inter acquiſitum maiori et ac­
                  <lb/>
                quiſitum minori erit minor ꝓportio quam inter
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                datos terminos. </s>
                <s xml:id="N154BC" xml:space="preserve">Patet hoc correlarium ex prio­
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                ri demonſtratione paucis mutatis.
                  <note position="left" xlink:href="note-0054-02a" xlink:label="note-0054-02" xml:id="N155EB" xml:space="preserve">5. correl.</note>
                </s>
                <s xml:id="N154C6" xml:space="preserve">¶ Sequit̄̄ quī­
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                to /  quando inter aliquos terminos eſt propor-
                  <lb/>
                tio maioris inequalitatis: et vtro decreſcente in­
                  <lb/>
                ter deperditum a maiori termino et deperditum
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                a minori eſt minor ꝓportio quam inter datos ter­
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                minos. </s>
                <s xml:id="N154D3" xml:space="preserve">tunc ꝓportio inter datos terminos maio­
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                ratur: et ſi ſit maior ꝓportio inter illa deperdita
                  <lb/>
                proportio inter datos terminos diminuitur. </s>
                <s xml:id="N154DA" xml:space="preserve">Ex-
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                emplum / vt capto bipedali et pedali: ſi bipedale ꝑ­
                  <lb/>
                dat pedale: et pedale quartam pedalis: tunc pro-
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                tio inter datos terminos diminuitur: quia in fine
                  <lb/>
                talis diminutionis illorum terminorum manet ꝓ­
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                portio ſexquitertia quatuor quartarum videlicet
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                ad tres quartas et ſi bipedale perdat pedale et pe­
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                dale tres quartas ꝓportio maioratur: </s>
                <s xml:id="N154EB" xml:space="preserve">Manet eī
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                in fine ꝓportio quadrupla vnius pedalis ad q̈r-
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                taꝫ. </s>
                <s xml:id="N154F2" xml:space="preserve">Probatur / ſit .ab. maior terminus .cd. minor /
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                inter quos ſit proportio f. / et inter a. et c. partes il-
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                lorum terminorum ſit ꝓportio g. minor ipſa pro-
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                portione f. et deperdat .ab. ipſam a. partem et .cd.
                  <lb/>
                c. partem: tunc dico /  in fine talis deperditionis
                  <lb/>
                ꝓportio inter illos terminos augetur: ita  pro-
                  <lb/>
                tio b. ad d. qui ſunt termini manentes eſt maior ꝓ­
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                portione f. </s>
                <s xml:id="N15503" xml:space="preserve">Quod probatur ſic / quia facta tali di-
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                minutione in vtro illorum terminorum: manet
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                preciſe proportio inter b. et d. et illa eſt maior ꝓ-
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                portione f. / igitur propoſituꝫ. </s>
                <s xml:id="N1550C" xml:space="preserve">Maior eſt nota cuꝫ
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                conſequentia: et probatur minor: et ſit h. vna lati­
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                tudo ad quam a. ſe habet in ꝓportione f. / et arguo
                  <cb chead="Capitulum octauum"/>
                ſic ſi quando .ab. perdit a.cd. perdit h. / tunc inter
                  <lb/>
                illos terminos maneret ꝓportio f. / vt patet ex ter­
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                tio correlario quinte concluſionis ſecundi capitis
                  <lb/>
                huius partis: ſed modo quando .ab. perdit a.cd.
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                perdit c. quod eſt maius ipſo h. / ergo ipſum .cd. qñ
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                perdit c. manet minus quam quando deperdit h.
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                et ex conſequenti ipſius b: ad id quod manet deꝑ-
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                dito c. ab ipſo .cd. puta ad ipſum d. eſt maior pro-
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                portio quã ipſius b. ad id quod manet ex ipſo .cd.
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                deperdito h. </s>
                <s xml:id="N15528" xml:space="preserve">Patet conſequentia ex ſe: et ex con-
                  <lb/>
                ſequenti ſequitur /  proportio b. ad d. eſt maior ꝓ­
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                portione f. / quod fuit probanduꝫ. </s>
                <s xml:id="N1552F" xml:space="preserve">Sed iam probo
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                illam minorem videlicet /  quando .ab. ꝑdit a.cd.
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                perdit c. / quod eſt maius ipſo h. </s>
                <s xml:id="N15536" xml:space="preserve">Quod ſic proba-
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                tur / quia ipſius a. ad ipſum h. eſt maior proportio
                  <lb/>
                quam eiuſdem a. ad ipſum c. / vt patet ex caſu / igit̄̄
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                c. eſt maius ipſo h. / quod fuit oſtendendum. </s>
                <s xml:id="N1553F" xml:space="preserve">Patet
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                conſequentia / quia eiuſdem ſemper eſt maior pro­
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                portio ad minus quam ad maius. </s>
                <s xml:id="N15546" xml:space="preserve">Et ſic patet pri­
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                ma pars. </s>
                <s xml:id="N1554B" xml:space="preserve">Secunda pars probatur: ſint .ab. termi­
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                nus maior .cd. minor inter quos ſit ꝓportio f. et in­
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                ter a. et c. ſit proportio g. maior ꝓportione f. et de­
                  <lb/>
                perdat .ab.a. et .cd.c. / ita  in fine maneat preciſe
                  <lb/>
                proportio inter b. et d. / et tunc dico /  in fine illa ꝓ­
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                portio ipſius b. ad d. manet minor f. </s>
                <s xml:id="N15558" xml:space="preserve">Quod ſic ꝓ-
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                batur: et volo /  quando .ab. perdit a.cd. perdat
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                h. ad quam latitudinem h.a. habet ꝓportionem f. / et
                  <lb/>
                arguo ſic / ſi quando .ab. perdit a.cd. perderet h. /
                  <lb/>
                tunc illi termini manerent in eadem proportione
                  <lb/>
                puta f. / vt patet ex tertio correlario quinte conclu­
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                ſionis ſecundi capitis huius: ſed modo in caſu cõ­
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                cluſionis quando .ab. ꝑdit a.cd. perdit c. / quod eſt
                  <lb/>
                minus ipſo h. / ergo ipſum .cd. quando ꝑdit c. ma-
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                net maius quam quando perdit h. / et ex conſequē-
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                ti ipſius b. ad id quod manet deperdito c: a.cd. eſt
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                minor proportio quam ſit f. que eſt ipſius b. ad id
                  <lb/>
                quod manet ex .cd. deperdito h. / quod fuit proban­
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                dum. </s>
                <s xml:id="N15575" xml:space="preserve">Sed iam probo /  c. ſit maius ipſo h. / q2 ipſi-
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                us a. ad ipſum h. eſt maior proportio quam eiuſ-
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                dem a. ad ipſum c. ex hypotheſi: ergo ipſum c. eſt
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                maius ipſo h. / quod fuit oſtendendum. </s>
                <s xml:id="N1557E" xml:space="preserve">Patet con­
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                ſequentia vt prius et per conſequens correlariuꝫ
                  <lb/>
                  <note position="right" xlink:href="note-0054-03a" xlink:label="note-0054-03" xml:id="N155F1" xml:space="preserve">6. correĺ.</note>
                </s>
                <s xml:id="N1558A" xml:space="preserve">¶ Sequitur ſexto /  quando inter aliquos termi-
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                nos eſt ꝓportio maioris inequalitatis: et decre-
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                ſcente vtro termino ꝓportio inter eos augetur:
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                tunc deperditi a maiori termino ad deperdituꝫ a
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                minori eſt minor ꝓportio quam ſit proportio īter
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                datos terminos in principio talis diminutionis.
                  <lb/>
                </s>
                <s xml:id="N15598" xml:space="preserve">Et ſi vtro illoruꝫ decreſcente: ꝓportio inter eos
                  <lb/>
                diminuitur: tunc deperditi a maiori termino ad
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                deperditum a minori eſt maior ꝓportio / quam ſit
                  <lb/>
                ꝓportio inter datos terminos in principio talis
                  <lb/>
                diminutionis. </s>
                <s xml:id="N155A3" xml:space="preserve">Hoc conuerſum precedentis corre-
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                larii ex eius probatione facile oſtenditur paucis
                  <lb/>
                adiunctis. </s>
                <s xml:id="N155AA" xml:space="preserve">¶ Et circa predicta correlaria aduerte /
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                 ipſa moderanda ſunt cum maior terminus ma­
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                nens continuo maior maiorem latitudinem acqui­
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                rit vel deperdit quam minor: alias correlaria nõ
                  <lb/>
                erunt īmunia a falſitate: nec ſequentibus aliquo
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                modo ſeruirent.
                  <note position="right" xlink:href="note-0054-04a" xlink:label="note-0054-04" xml:id="N155F7" xml:space="preserve">7. correl.</note>
                </s>
                <s xml:id="N155BC" xml:space="preserve">¶ Sequitur ſeptimo /  datis duo­
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                bus terminis ſe habentibus in aliqua ꝓportione /
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                et capta aliqua parte maioris ſe habente ad cer-
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                tam parteꝫ minoris in ea ꝓportione in qua ſe ha­
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                bent dati termini: reſidua maioris et minoris ſe
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                habent etiam in eadem proportione dati termi-
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                ni exemplum / vt capto pedali et bipedali ſe habē-
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                tibus in ꝓportiõe dupla: et capta vna quarta ma­
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                ioris et altera quarta minoris que etiaꝫ ſe habēt
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                in proportione dupla: reſidua, puta tres quarte </s>
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